Predictive equations are a quick and non-invasive way to estimate a
patient's energy requirements, and can be a useful tool when used
appropriately. However, as with any tool, the skill and experience of
the user will affect the quality of the result. This paper looks at the
origins and limitations of some of the more commonly used equations.
Considerations in their use and interpretation, such as the use of
injury and activity factors, adjusting weight and non-protein calories,
are also discussed.

The estimation of a patient's requirements is an essential
component of nutrition support, ensuring that the patient's
nutritional needs are met without significant over- or underfeeding. In
everyday hospital practice, several different equations are used, often
without an adequate understanding of their origins and limitations.
(1,2) This can lead to significant variation in energy provision, which
could have serious implications for patient care. A previous review of
prediction equations concluded that none is sufficiently accurate to be
useful in practice. (3) However, the reality is that equations are the
most widely used method for assessing nutrition support that patients
need in hospital. When used appropriately, a predictive equation can be
a useful tool. Although it is not a 'magic formula' to tell us
the answer, it enables us to make a good prediction as a starting point for ongoing patient care. Like any tool, the equation is only as good as
the person using it: skill and experience will significantly inform the
use and interpretation of these prediction equations.

BASIC CONCEPTS

The body's energy expenditure is usually described as
consisting of three components: the basal metabolic rate (BMR), the
energy expended in physical activity, and the thermic effect of feeding
(TEF). The BMR is the minimum amount of energy required to sustain the
body's essential metabolic processes. It is the value for metabolic
rate that would be obtained when the subject first awakes (remaining
relaxed, and motionless) after an overnight fast, in a thermoneutral
setting. Resting metabolic rate (RMR) approximates the BMR when it is
not possible to meet all of the above conditions. It is usually measured
in a subject who has fasted and has been lying quietly for at least 30
minutes before measurement. (4) The TEF is the amount of energy consumed
by the body after eating, in digesting and absorbing the nutrients from
food and converting them for use or storage. It can be measured using
indirect calorimetry, by comparing the BMR with energy expenditure
measured (in the same conditions) after a meal. TEF is usually assumed
to be about 10-15% of the BMR, but is affected by a wide range of
factors, such as the subject's nutritional status and the
composition of the diet. Other terms used for the TEF include:
'diet-induced thermogenesis', 'postprandial
thermogenesis', and 'thermic effect of a meal'. (5) The
total energy expenditure is the total of basal energy expenditure (BMR),
the TEF and activity. Increased activity raises the total, as does
increased food intake (by increasing TEF) and illness/inflammation (by
increasing BMR).

The rate of energy consumption in the body changes from moment to
moment, and varies between different body organs and tissues, but an
individual's BMR changes very little, even over significant periods
of time. (6,7) Metabolic rate measurements produce a
'snapshot' of energy expenditure over a short period, which is
then used to estimate the average rate of energy expenditure for the
whole day. However, the measurement period may not reflect the true
energy expenditure, as there is necessarily some variation and error
involved. Similarly, the energy released from food will not provide
exactly the calculated amount, because of losses as unabsorbed nutrient,
losses due to energy conversion inefficiencies, and losses as heat.
Decreased activity and muscle mass with ageing, and smaller muscle mass
in women, generally contribute to a lower energy expenditure; however,
variation between individuals is significant. A group of people of the
same age and sex who have similar body weight and body composition will
not have identical BMRs; even when intake and activity are controlled,
the variation in BMRs between different members of the group will be as
much as 10%. (8)

EQUATIONS FOR ESTIMATING ENERGY REQUIREMENTS

Clearly, it would be best if it were possible to measure actual
energy expenditure, rather than just estimating it. For this reason,
indirect calorimetry is considered to be the 'gold standard'
for assessing energy expenditure in hospitalised patients. This uses
respiratory gas exchange to estimate fuel consumption, and can produce
accurate results when implemented correctly by trained personnel. It is
not infallible, however, as its results are affected by factors such as
oxygen therapy, haemodynamic instability, fever, nursing care activities
and difficulties obtaining a steady state. (9) It is time-intensive and
requires expensive equipment, and at present, most dietitians do not
have access to this method for everyday estimation of their
patients' needs.

Other measurement methods are generally not useful for hospital
patients. Direct calorimetry is not in wide use even for research
purposes, as it measures energy expenditure by monitoring the
body's heat production and requires a specially designed sealed
room with tightly controlled conditions. The doubly labelled water
technique is the only research method that allows energy expenditure to
be estimated in free-living subjects. This uses orally administered
'heavy' water (containing stable isotopes of hydrogen and
oxygen) to measure the body's carbon dioxide production as
indicated by the gradual loss of the isotopes from the body over 1-3
weeks. (4) The energy expenditure can then be estimated in a similar way
to that in indirect calorimetry. The time frame for doubly labelled
water studies is too long for the assessment of most hospital patients,
and the heavy water is expensive. As an alternative to these measurement
methods, predictive equations provide a cheap, quick and non-invasive
method for estimating requirements, based on the main factors that
affect energy expenditure: age and sex (which both affect body
composition), and body size.

Researchers developing predictive equations have attempted to
validate these against measurements of energy expenditure, often using
statistical regression or correlation. When assessing the literature, it
should be noted that correlation does not necessarily indicate how
closely the equation can estimate the patient's expenditure. For
example, if an equation always produced a result that was exactly double
the true energy expenditure, it would lead to dangerous over-feeding if
it was used for predicting patients' requirements. Statistically,
though, it is considered a perfect correlation, with a correlation
coefficient r = 1. The correlation therefore does not indicate how
useful the equation would be in practice. Validation of predictive
equations should always consider residuals, limits of agreement, or
other indication of fit, rather than just the correlation coefficient.
(10)

Various equations have been developed for the estimation of energy
requirements, but the most commonly used equations are the
Harris-Benedict equation and the Schofield equation. More recently
developed equations have attracted attention; these include the
Mifflin-St Jeor equation and the Ireton-Jones equation.

Schofield equation (11,12)

The Schofield equations are an extension of the FAO/WHO/UNU work on
energy requirements (13) and, as a result, are sometimes referred to,
incorrectly, as the WHO equation. (14) Having since been revised by
Schofield, the equation now in use is slightly different due to the
incorporation of some extra data. It is the most commonly used by
Australian dietitians (1) and has been preferred, because it does not
require a value for height and, therefore, introduces fewer sources of
error if no measured height or weight are available. Schofield did
develop an additional equation that included height, but it did not
significantly increase the accuracy of the prediction when compared with
the simpler equation. The Schofield equation (Table 1) estimates basal
requirement. It is based on a very large data set (pooled BMR data from
114 studies, with more than 7000 healthy subjects from 23 different
countries). The results may have been affected by significant
differences in ambient temperatures for some of the data, and also some
of the subjects were significantly underweight and may have been
malnourished. The age and weight range of subjects is wide, but the
group contains many more men than women, and a significant number (about
1000) of the subjects were young male Italian soldiers and cadets. The
average subject in Schofield's data set would therefore be
significantly younger, leaner and fitter than an average Australian
hospital patient. This may mean that the equations overestimate requirements (15,16) even in young healthy Australian men. (17) Other
validating studies have suggested that it may overestimate for those
with low requirements and underestimate for those with high
requirements, deviating towards the mean for both. (14) In 1991, a
British panel of experts, the Panel on Dietary Reference Values,
published a modified version of the Schofield equation for use in
Britain. (18) They added data from an additional 451 European subjects,
particularly from older age groups, and also excluded some of
Schofield's original data which were 'collected in the
tropics' and were not felt to reflect the requirements of
better-nourished British people. The original data set may in fact have
been more appropriate for multicultural Australia; however, the
modifications affect only the older (over 60 years) age group. In any
case, the majority of Australian dietitians are likely to be using the
original, unmodified equations, because these are generally the ones to
be found in textbooks and other widely used resources, such as the
Dietitians' Pocketbook, (19) the previous Recommended Dietary
Intakes for Use in Australia (20) and the Nutrient Reference Values for
Australia and New Zealand, which replaced it. (21)

Harris-Benedict equation (22)

This equation was developed from a single smaller study, with only
239 subjects, all healthy Americans. The participants may not be
reflective of modern Australians because they were relatively young
(average age 29 [+ or -] 11 years) and lean (average body mass index 21
[+ or -] 3 kg/[m.sup.2]). Repeated measurements were made in each
subject, with careful attention to factors such as subject inactivity;
however, the limitations of the testing conditions mean that some
subjects may not have been in a true 'basal' state, leading to
over-estimation of their energy needs. (8,15) The Harris-Benedict
equation (Table 2) is thought to overestimate requirements in healthy
people, perhaps by 5% in men or 15% in women. (23-25) A disadvantage of
this equation is that it requires both weight and height, which may
often not be available. However, as it remains the most commonly used
equation in the world, particularly in the USA, it is essential to be
familiar with it when assessing the medical literature.

Mifflin-St Jeor equation (26)

This equation used 498 healthy adult subjects with a wide range of
ages and weights (about half of the subjects were obese) and measured
resting metabolic rate. The equation uses actual weight, and notably it
predicts significantly lower requirements when weight is very high,
compared with the Schofield and Harris-Benedict equations. An advantage
of the Mifflin-St Jeor equation (Table 3) is that it is very simple and
easy to remember; however, like the Harris-Benedict equation, it
requires values for both weight and height. Because of its wider range
of subjects, it is considered to reflect the requirements of the modern
US population with less estimation bias than other equations, and has
recently been endorsed by the American Dietetic Association. (27) Its
use may increase in those populations among whom obesity is becoming
more common, but it does not yet appear to be in common use in Australia
(1) and has not been subjected to as much critical scrutiny as the older
equations, having been developed more recently Further research may help
establish whether it will be of lasting use in practice.

Activity and injury factors

All three of the equations above were developed using healthy
subjects, and may not accurately reflect the requirements of
hospitalised patients. They estimate only basal or resting requirements,
and therefore, it is customary to make adjustments to the value
obtained, to allow for energy expended in activity and for the increased
requirements due to illness. In practice, these adjustment factors are
often applied in different ways. Typically, the result from the equation
is multiplied by an activity factor (which may be only 1.0 for a sedated
patient lying still in bed) and a stress or injury factor pertaining to
the individual patient's condition. There is no evidence to support
the less-common practice of adding the activity and stress factors
before multiplying by the basal energy expenditure. It may be based on
different assumptions about how activity and stress would increase
requirements.

The activity and stress factors were not developed by the authors
of the equations, but have been suggested by researchers investigating
total energy expenditure in different states of illness or exercise.
Table 4 lists activity factors derived from the FAO/WHO/UNU Expert
Consultation Report and from a variety of other studies, mostly in
healthy people. (13,28-33) Physical activity levels (PALs) are obtained
by measuring total energy expenditure in free-living individuals and
dividing by their BMR. This produces a multiple of the BMR that
expresses the average energy requirement for that individual's
level of daily activity. When the measured energy cost of a particular
activity (climbing a ladder, for example) is expressed as a multiple of
BMR, this is called the physical activity ratios (PARs) for that
activity. Both PALs and PARs are expressed as a multiple of the BMR, and
are therefore affected by any errors in measurement of BMR and total
energy expenditure. (34) The PAR and PAL values are generated from
non-fasting subjects, so they include the TEF: this means that an
additional factor for TEF is not necessary when using these as activity
factors to predict an individual's energy requirement. Illness may
have an effect on TEF: the thermic response to nutrition can be
increased in stress situations, while continuous tube feeding may reduce
TEF close to the fasting level. (9) It is important to consider that
illness and sedation cause a decrease in activity, so the activity
component of total energy expenditure is likely to be lower for a
hospital patient than for a healthy person performing the same activity.
For example, studies of healthy people with sedentary jobs found that
their activity factor averaged 1.5-1.7, (29,35) while Elia reports a
variety of studies showing activity factors of only 1.15-1.3 in
free-living people with chronic illnesses, and 1.0-1.2 in hospitalised
people with acute diseases. (28)

Although illness tends to cause a decrease in physical activity, it
can also cause an increase in energy requirements, by several different
mechanisms. For example, inflammatory or infective illness can increase
the BMR. Large wounds, such as in burn injury, cause loss of heat and
body tissue. A fever may increase energy expenditure by about 10% of BMR
for every centigrade degree above normal body temperature, (36) while
inducing hypothermia (such as after stroke or cardiac arrest) decreases
energy expenditure. (37) Pain and stress, too, increase energy
expenditure, while sedation and pain control can decrease it. Energy
expenditure is reduced further with heavier sedation. (38)

Since the early studies of energy expenditure were published,
changes in patient care (particularly in the critically ill) such as
improved pain management and respiratory support, avoidance of
overfeeding, and more effective treatment of infections, have reduced
the impact of illness on energy consumption. This means that older
recommendations for injury factors are mostly too high. Newer research
has also revealed a surprisingly wide variation in metabolic rates of
patients with conditions that were previously assumed to be consistently
hypermetabolic, such as cancer (39) and sepsis. (40,41) Such patients
may have BMRs that are close to normal, or even below normal, and even
where hypermetabolism occurs, it may be short-lived, peaking within a
few days. (28) Unfortunately, the injury factors that are still in wide
use (and which still appear in many textbooks) are those from the
original classic paper by Long et al. from 1979, (42) and use of these
may significantly overestimate requirements, as indicated by more recent
studies. (28,43-45) One of the more comprehensive approaches is the
study by Barak et al., (43) who derived injury factors for the
critically ill using indirect calorimetry and compared them with
existing factors in the literature. The paper by Elia (28) is a
compilation of energy expenditure data for a variety of both acute and
chronic illnesses. Table 5 displays some injury factors based on these
recent studies.

The studies that derived these injury factors have most commonly
used the Harris-Benedict equation, and consequently it has been argued
that the factors are not valid to use with other equations. However, the
injury factors represent the estimated degree of hypermetabolism as a
multiple of the BMR, so in theory they should be applicable to any
equation that accurately estimates BMR. In reality, none of the
equations is free of bias or error, and this error may be increased if
the injury factors are treated as fully transferable between equations.
Even with equations known to have a similar bias (such as the Schofield
and Harris-Benedict equations, which both tend to overestimate BMR)
conservative selection of activity and injury factors may be necessary,
to avoid overfeeding. Careful evaluation of the individual patient, with
attention to biochemical parameters (such as albumin, C-reactive
protein) and clinical signs (such as body temperature, minute
ventilation, cardiac output, weight changes), can also help identify
whether hypermetabolism is likely, justifying the use of a larger injury
factor.

In critically ill patients, even when the energy requirement is
significantly increased, it may be difficult, and even inappropriate, to
meet these needs. Stress metabolism can interfere with utilisation of
the extra energy, leading to an increased risk of overfeeding, and
undesirable complications. (46) Conservative provision of nutrition
support, or even deliberate underfeeding, is increasingly being
recommended in these patients (47,48) despite their known increase in
requirements.

Ireton-Jones equation (49)

This is one of the few equations available that have been developed
and validated for use in hospitalised patients, rather than healthy
people, and is notable for its lower estimates for heavier patients when
compared with other commonly used equations. (50) The original equation
(Table 6) was developed from a single study of 200 hospitalised
patients, including patients with trauma and burns. Advantages of the
Ireton-Jones equation include the fact that it uses the patient's
actual weight, does not require a value for height, predicts total
energy expenditure (therefore does not require activity or stress
factors), and is subject to ongoing review by its authors and,
therefore, may be more reflective of contemporary medical management
than other, older equations. It takes into account specific clinical
conditions, such as mechanical ventilation or trauma. However, it is
important to be aware of the many assumptions made in developing this
equation, which affect its use and interpretation. These include:

1 A patient is critically ill only while ventilated.

2 All burns and trauma are of the same severity, and affect energy
requirement during the ventilated/critical illness phase only. This
means that the equation does not account for an anabolic period of
convalescence.

3 All modes of ventilation have the same impact on energy
requirements.

4 All obese patients have the same body size and body composition
at a given weight.

Several study groups have tested this equation on their own
patients, usually by comparing the results of the equation (which
estimates total energy expenditure) with indirect calorimetry measures
of resting expenditure. This may be appropriate in a sedated critically
ill patient, but is not a valid comparison if the patient has
significant activity. Unsurprisingly, the Ireton-Jones equation produces
a result that is significantly greater than the resting energy
expenditure in such situations. (51,52) In a number of studies of
sedated mechanically ventilated patients, the Ireton-Jones equations
performed better than other equations (including the Harris-Benedict
equation), but did show some bias towards underestimation. (50,53-56)
Two studies of acutely ill hospital patients found that the
Harris-Benedict equation used with an injury factor was more accurate
than the Ireton-Jones equation. One of these studies looked at
normal-weight ventilated critically ill patients (using a factor of
1.2); (55) the other was in acutely ill obese patients and used an
adjusted weight value (with an injury factor of 1.3). (57)

OTHER CONSIDERATIONS

Adjusting weight

Which value to use for body weight has been a controversial issue
for some time. All of the equations discussed above were developed using
the actual weight of each subject, and the authors make no
recommendations regarding the use of any other value. Use of an
arbitrary adjusted weight value introduces an additional source of
possible error, increasing the variability of the result. (58) However,
there are many situations in which the patient's weight differs
significantly from normal, and the use of the actual weight value can
lead to unacceptable errors in estimating requirements. (59-61) It may
therefore be appropriate sometimes to use a different value in the
calculation.

If the patient is underweight, the use of the patient's
current weight is likely to be the best way to estimate current energy
requirements. However, in some patients, such as the critically ill,
this may be an underestimate. (59) If it is appropriate to aim for
weight gain, ideal weight can be used to estimate an ideal energy
intake. However, this approach may be too aggressive for frail or
unstable patients, and it may be necessary to select a more conservative
goal weight at first, particularly in very underweight people. Close
monitoring is desirable to ensure that the patient does not develop
overfeeding-related complications. The risk of overfeeding is increased
during illness, as stress metabolism alters fuel utilisation. (46)
During this time, any weight gained will be mainly fat and fluid. (62)
As a guide, weight change (either gain or loss) is not an appropriate
goal during the period that an injury/stress factor applies to the
patient.

If the patient is overweight or obese, or severely oedematous,
using the actual weight can lead to an overestimation of the
patient's requirements. The metabolic activity of adipose tissue is
lower compared with other tissue, (63,64) so an obese patient has a
lower metabolic rate per kg body weight. It has been suggested that the
ratio of lean tissue to fat tissue changes as weight increases. That is,
an increase in adipose tissue is supported by an increase in muscle and
organ mass but, at the point of obesity, the fat stores are increasing
disproportionately. (65,66) Studies using indirect calorimetry have
obtained conflicting results on this point. (23-26,43,67,68) Some
suggest that the ratio of lean tissue to fat tissue remains the same as
weight increases, even in obesity; others indicate that equations using
actual weight can grossly overestimate requirements in the obese. Use of
an adjusted weight value is clearly problematic, (69) but may still be
appropriate in order to avoid overestimating the patient's
requirements in cases where overfeeding is particularly undesirable.
These may include situations such as:

1 Where an obese or oedematous patient is not mobilising, such as
bedbound or critically ill patients. An ambulant obese or oedematous
patient has greater energy expenditure in everyday activities as a
result of moving the extra body weight around. If the patient is not
mobilising, this contribution to energy expenditure is absent.

2 Where overfeeding may be difficult to detect and is very
undesirable, such as in mechanical ventilation or other respiratory
compromise, or patients receiving parenteral nutrition.

3 Where the patient is sedentary in the long term, and muscle is
not being maintained by activity (therefore, any extra weight is more
likely to be adipose tissue), such as elderly patients or those who are
otherwise mobility disabled.

4 In patient groups with known reduced energy needs, such as head
injury patients after the acute period.

Usually the adjustment consists of using the ideal weight plus
25-50% of the excess weight. (43,57,67) For example, a patient weighing
100 kg whose ideal weight is 60 kg would have an adjusted weight value
of 70-80 kg for use in predictive equations. Ideally, the choice of
weight adjustment should be based on a physical assessment of the
patient's tissue stores. A very muscular patient can be
'overweight' yet be very lean, and it would be appropriate to
use actual weight in predicting the energy requirement. For most
patients requiring an adjusted weight calculation, an average between
ideal and actual weights would be appropriate, (43,57) while in extreme
adiposity, where lean tissue stores appear depleted, or in oedema, where
lean tissue is not contributing to the extra weight, an even lower
adjusted weight might better reflect the patient's reduced
metabolic activity. (67) Using an adjusted weight value requires
caution, as it increases the risk of underfeeding in overweight
patients. (27) If the patient is ambulant, it may be more appropriate to
use an obesity-validated equation, such as the Mifflin-St Jeor equation
(if height information is available) or the Ireton-Jones equation using
the obesity factor.

Total energy or 'non-protein calories'?

In the past it has been suggested (most commonly in the context of
parenteral nutrition) that a patient's energy requirements should
be provided as 'non-protein calories', in order to spare the
protein for healing and anabolism. However, predictive equations
estimate the consumption rate of all energy, not just non-protein
energy. If it is assumed that the estimated requirement refers only to
the non-protein energy requirement, overfeeding will result, and beyond
a certain point, giving extra energy will not improve protein sparing at
all. As long as the protein requirement is met, it is sufficient to
provide the estimated energy needs as the total energy input. (70,71)

CONCLUSION

The use of predictive equations for energy requirements has many
pitfalls. There is little benefit in blindly applying an equation
without paying attention to the individual characteristics of the
patient and the situation. This can affect the credibility of the
nutrition support dietitian, attracting terms like
'mumbo-jumbo' and 'dietitian's fudge factor'.
An understanding of the origins and limitations of the equations is
important for any dietitian who uses them.

The complex appearance of the equations unfortunately seems to give
them more authority than they deserve. An equation is not a magic
formula, and will not transform incorrect or inaccurate data into a
useful result. For example, using an equation with both an estimated
height and an estimated weight is probably no better than just making a
conservative guess about an appropriate feed rate, or approximating
requirements with a simple rule of thumb (such as a
'calories-per-kilo' method). Expressing the predicted
requirement as a range, rather than a fixed value, may help avoid
implying an unrealistic level of accuracy.

Most importantly, it is often forgotten that the equation only
provides a suggested starting point for energy provision: the aim is not
just to obtain the 'right answer' at the beginning and then
walk away. Ongoing monitoring of the patient is essential, and this may
involve regular re-estimation of requirements and adjustment of the
feeding regimen as the patient's condition changes. An equation
cannot replace other forms of assessment, such as physical examination,
and is no substitute for quality patient care. However, when used by an
informed and experienced practitioner, predictive equations can still be
a valuable and time-saving tool, and retain a role in a dietitian's
evidence-based clinical practice.

ACKNOWLEDGEMENTS

The authors wish to acknowledge Kathryn Marshall, Nicola Riley and
Kellie Draffin for their valuable contributions to this paper.

18 UK Department of Health. Report on health and social subjects
41: dietary reference values for food energy and nutrients for the
United Kingdom. Report of the Panel on Dietary Reference Values of the
Committee on Medical Aspects of Food Policy. London: Her Majesty's
Stationery Office; 1991.

20 National Health and Medical Research Council (NHMRC).
Recommended Dietary Intakes for Use in Australia. Canberra: National
Health and Medical Research Council, 1991.

21 National Health and Medical Research Council (NHMRC) and New
Zealand Ministry of Health. Nutrient Reference Values for Australia and
New Zealand. Canberra: National Health and Medical Research Council,
2006.